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It is predicted that for sufficiently strong electron-phonon coupling ananomalous quantum chaotic behavior develops in certain types of suspendedelectro-mechanical nanostructures, here comprised by a thin cylindrical quantumdot (billiard) on a suspended rectangular dielectric plate. The deformationpotential and piezoelectric interactions are considered. As a result of theelectron-phonon coupling between the two systems the spectral statistics of theelectro-mechanic eigenenergies exhibit an anomalous behavior. If the center ofthe quantum dot is located at one of the symmetry axes of the rectangularplate, the energy level distributions correspond to the Gaussian OrthogonalEnsemble (GOE), otherwise they belong to the Gaussian Unitary Ensemble (GUE),even though the system is time-reversal invariant.Comment: 4 pages, pdf forma

Anomalous quantum chaotic behaviour in suspended electromechanical nanostructures